Theory Group, Physical Research Laboratory, Navrangpura, Ahmedabad 380 009, India E-mail: saurabh@prl.res.in
Abstract. The talk described the prospects of studying standard model parameters as well as scenarios beyond the standard model, like the minimal supersymmetric standard model, theories with extra dimensions and theories with extra neutral gauge bosons, at a future lineare+e−collider.
Keywords. Linear collider; standard model; physics beyond the standard model.
PACS Nos 13.66.Jn; 13.66.Hk; 13.66.Fg
1. Introduction
1.1 The need for ane+e− collider
The large hadron collider (LHC) colliding protons on protons at a centre-of-mass (cm) energy of 14 TeV will become operational next year. It will look for the Higgs boson, the missing link of the standard model (SM), and also for new physics beyond the standard model (BSM). However, while LHC will be a good tool to discover new physics, it is generally realized that for precision measurements of parameters of various theories, there is need for a high luminositye+e− collider operating at a cm energy of at least a few hundred GeV [1]. It would thus be complementary to hadronic colliders.
An inherent advantage of an e+e− collider is a smaller hadronic background.
Hence, higher accuracy for a lower energy is possible. Here it is appropriate to recall the success of LEP in making precise measurements of the couplings of the Z and other SM parameters. Another advantage of an e+e− collider is that the energy of the incoming particles is fixed and tunable, unlike the energies of partons participating in a hadronic collision.
The other advantage of a linear collider is that there is the possibility of having γγ,γeande−e− as additional modes, which can provide qualitatively and quanti- tatively different information. A further option known as the GigaZ option can be used to improve on the accuracy of LEP with the use of a higher luminosity with the energy tuned to theZ resonance.
1.2 Features of ane+e− collider 1.2.1 Parameters of the collider
The centre-of-mass (cm) energy of the linear collider would range from 300 to 1000 GeV. It would be expected to operate just above the tt threshold for the study of the top mass, and at √
s = 500 GeV for most of the remaining data.
Studies show that it would be useful to operate it at a higher cm energy like 800 or 1000 GeV at a higher luminosity for studying certain processes. The expected luminosity is a few times 1034 cm−2 s−1 at 500 GeV, which is equivalent to an integrated luminosity of 500 fb−1after a run of a couple of years or so. As mentioned earlier, it may be operated at √
s = mZ (GigaZ option). It seems possible to have a high degree of longitudinal beam polarization for e− as well as e+. An International Technology Recommendation Panel took a decision that the collider would be built based on ‘cold’ (superconducting) technology, rather than ‘warm’
(room temperature) technology.
1.2.2 Options at the ILC
A number of options have been suggested for ILC. First of all, it could be run in e+e− or e−e− modes. This would realize qualitatively different physics goals.
There could also be quantitative differences on account of different backgrounds in the two cases.
The other kind of option arises because the beams can be polarized. e−as well as e+beams could be longitudinally polarized, though the technologies in the two cases are different. The anticipatede− polarization is 80–90%, whereas the anticipated e+polarization is around 60%. Longitudinally polarized beams can help to reduce background as well as improve sensitivity [2]. While for many purposes the presence ofe− polarization alone helps, the availability ofe+ polarization at the same time is essential for some processes [2]. In the case of longitudinal polarization, the effective polarization for most processes is the combination
Peff = (Pe−−Pe+)/(1−Pe−Pe+). (1) This can be larger than individual polarizations, depending on their relative signs.
It is nonzero, and equal toPe− even whene+ polarization is zero.
It is also possible to convert longitudinal polarization to transverse polarization using spin rotators. Transverse polarization, through azimuthal distributions, helps to provide qualitatively different information as compared to longitudinal polariza- tion [2].
It has been pointed out that Compton backscattering of high-intensity laser beams off high-energy electron beams can give photon beams which carry a large fraction of the electron energy [3,4]. Figure 1, taken from [3], shows the spectrum of photons expected from laser backscattering. It can be seen that if the product of the laser photon helicity Pc and the electron helicity λe is negative, the spec- trum is highly peaked at a large value of the ratio y of the photon energy ω to
Figure 1. The spectrum of photons ob- tained by backscattering of a laser beam off high energy electrons (from [3]).
Figure 2. The polarization of photons produced by backscattering a polarized laser beam off polarized high energy elec- trons (from [3]).
the electron energyE0. Polarized laser and electron beams can give high degree of photon polarization for a certain choice of laser photon and electron polarizations, as shown in figure 2, taken from [3]. In addition it would also be possible to have e±γcollisions.
2. Standard model physics at the linear collider 2.1 Gauge-boson self-interactions
The primary goal of studying gauge-boson self-interactions is to establish the non- Abelian nature of electroweak interactions. Processes sensitive to triple-gauge cou- plings aree+e− →W+W−ande+e− →W±e∓ν. These have already been studied at LEP2. In view of the much higher luminosity available at ILC, the accuracy of measurement would be greater. At high luminosity and with the help of beam po- larization, triple gauge couplings can be determined with an error of a few×10−4. The accuracy for different anomalous couplings is shown in table 1, taken from [5].
Neutral gauge boson anomalous couplings can be determined to the same precision ine+e− →γZ, ZZ. Asymmetries with longitudinal or transverse polarization can be used for CP-odd couplings [6].
2.2 Top-quark production at threshold
Top-quark mass measurement can be made in top-quark pair production in the threshold region. The top mass can be measured precisely from a scan of the tt¯
Table 1. Limits on various anomalous couplings at ILC (from [5]).
√s= 500 GeV √
s= 800 GeV
∆gZ1 15.5 12.6
∆κγ 3.3 1.9
λγ 5.9 3.3
∆κZ 3.2 1.9
λZ 6.7 3.0
g5Z 16.5 14.4
g4Z 45.9 18.3
˜
κZ 39.0 14.3
˜λZ 7.5 3.0
Figure 3. Dependence of the e+e− → ttcross-section on √
s. The curves labelled LL (dotted), NLL (dashed), and NNLL (solid) include leading loga- rithmic, next-to-leading logarithmic, and next-to-next-to-leading logarithmic contributions, respectively. The three curves for each set of corrections repre- sent the variation of the rate with changes of the renormalization scale. This figure uses a threshold mass definition for the top quark mass [9] (from [7]).
threshold (√
s ≈340–380 GeV). Theoretical analysis of the cross-section needs a double-expansion ofσt¯tinαsand β=p
1−4m2t/s, the velocity of the top quark.
Terms up to next-next-to-leading order (NNLO) have been calculated [7,8]. It is found that simultaneous precision measurement ofmtandαswill be possible. Fig- ure 3 shows the calculated cross-section for e+e− → tt near the threshold in the leading logarithmic, next-to-leading logarithmic and next-to-next-to-leading loga- rithmic approximations, taken from [7], using a threshold mass definition for the top quark from [9]. With a 10-point scan, the expected precisions in the top mass,αs, and the width of the top quark are, respectively, ∆mt= 42 MeV, ∆αs(MZ) = 0.001,
∆Γt = 50 MeV. Including theoretical uncertainties, the precision expected is
∆mt(M S) = 100 MeV [10].
Figure 4. The Higgsstrahlung andW W fusion production cross-sections vs.
the Higgs mass for√
s= 300 GeV, 500 GeV and 800 GeV (from [11]).
2.3 Search for the SM Higgs boson
Search for the Higgs boson is of high priority at the LHC and the ILC. Once the Higgs is found, measuring its properties will be necessary for understanding the origin of gauge symmetry breaking and masses of various particles. To test the completeness of the minimal SM and the Higgs mechanism as the source of mass, measurements must show the following:
• Couplings of the Higgs boson to fermions and gauge bosons are proportional to their masses. This needs measurement of branching ratios.
• The Higgs boson has quantum numbersJCP= 0++.
• The Higgs boson is the source of its own mass. This needs the measurement of trilinear and quartic self-couplings.
The Higgs boson can be produced at a linear collider through ‘Higgsstrahlung’
(the Bjorken mechanism): e+e− → ZH, W W fusion: e+e− → νeν¯eH, or ZZ fusion: e+e− → e+e−Z. Figure 4 shows the production cross-sections for the former two processes. At √
s = 500 GeV, Higgsstrahlung dominates for mH<
∼160 GeV, whereas W W fusion dominates for mH>
∼160 GeV. For√ s= 800 GeV, the dominant mechanism isW W fusion. ZZ fusion contributes 10% at√
s= 800 GeV.
2.4 Measuring Higgs couplings
To distinguish the SM Higgs from the Higgs of an extended model it is necessary to measure Higgs couplings with precision. For this it is necessary to measure various decay branching ratios. Figure 5 shows the branching ratio and total width of a SM Higgs as a function of its mass.
FormH <150 GeV,H →b¯b dominates. Coupling to the bottom quark can be determined to a precision of about 2%. Couplings to the charm quark and τ can be determined to a precision of about 12% [12]. Coupling to the muon is expected to be poorly measured, to about 30% [13].
The top quark, being much heavier than other quarks, can play a special role.
FormH<2mt, the Higgs coupling to the top can be measured through
Figure 5. Branching ratios (left) and the total width (right) of the SM Higgs as a function of its mass (from [11]).
e+e− →t¯tH. (2)
This suffers from small rate and requires higher energy and luminosity. For√ s&
800 GeV and L ≈ 1000 fb−1, the Higgs coupling to the top can be measured to 10% accuracy [14].
2.5 Measurement of Higgs self-couplings
Higgs self-couplings in SM are described by the terms in the scalar potential:
V =1
2m2HH2+λ3vH3+1
4λ4H4. (3)
To establish the correctness of these terms, one needs to check the relation:
λ3=λ4=m2H/(2v). (4)
Measuring λ3 (λ4) requires the production of 2 (3) Higgs bosons through dou- ble (triple) Higgsstrahlung. For √
s = 500 GeV, and an integrated luminosity of 1000 fb−1,λ3can be determined to 20% accuracy throughe+e−→ZHH,H →b¯b, for 120 GeV< mH<140 GeV [15]. λ4is not easy to determine because of the small rate fore+e− →ZHHH [16].
2.6 Spin of the Higgs
For the SM Higgs it is necessary to verify that it has spin 0 and its CP even nature.
The angular distribution of Z in e+e− → ZH for a JP = 0+ Higgs should be dσ/d cosθ ∼sin2θ [17]. The spin can be determined from the √
s dependence of the cross-sectionσ[18]. Figure 6 shows the√
sdependence ofσfor the values 0, 1
Figure 6. The dependence of the cross-section for Higgs production via e+e−→ZH for values of the Higgs spins= 0,1 and 2 (from [18]).
and 2 for the spin of the Higgs. The spin can be determined from the invariant mass of the virtualZ in the decayH →Z∗Z formH <2mZ. The angular distribution of decay products in H → Z∗Z can distinguish P = + from P =− [19]. These measurements are near theHZ threshold, and require low luminosity (∼20 fb−1).
Finally, the observation ofH →γγ will rule outJ = 1.
2.7 Parity of the Higgs
The CP property of the Higgs can best be tested in theγγoption [20]. For linearly polarized photons, an even-parity Higgs is produced when the photons have parallel spins, whereas an odd-parity Higgs can be produced when the photons have spins perpendicular to each other.
3. Search for new physics at the linear collider
3.1 Anomalous top couplings in continuum pair production
Anomalous top couplings to γ, like anomalous magnetic and electric dipole mo- ments, would give evidence for beyond SM effects. Analogous dipole couplings to Z, called weak dipole couplings, are also possible. By suitable choice of angular or energy asymmetries, a sensitivity of 10−3×e/mt is possible for anomalous dipole couplings, with longitudinally polarized beams [21,22]. It is also possible to study anomalous couplings toγat aγγ collider [23–25].
3.2 Higgs in extensions of SM
The simplest extension of the Higgs sector is a two-Higgs doublet model. MSSM is a special case, with constrained couplings. With two Higgs doublets, the spectrum
consists of five scalars: H, h, A (neutral), H± (charged). When there is no CP violation,H, hhave CP= +,Ahas CP=−. If there is CP violation, there is mixing amongH, handAto give mass eigenstatesH1, H2, H3 which have no definite CP.
3.2.1 Higgs spectrum in MSSM
In MSSM at tree level, there are only two independent parameters because of the relations:
mh≤mZ, mA≤mH, m2H± =m2A+m2W, m2h+m2H=m2A+m2Z. (5) Radiative corrections change these relations. A recent analysis, including full one- loop corrections and the two-loop corrections controlled by αs and the Yukawa couplings of the third generation fermions gives an upper bound mh . 152 GeV [26].
3.2.2 Higgs production in MSSM
The CP-even HiggsesH, hare easily observable through Higgsstrahlung
e+e− →Z+H, h (6)
orW W, ZZ fusion,
e+e− →νν¯+H, h, e+e−→e+e−+H, h. (7) They can also be produced associated with the CP-oddA:
e+e− →A+H, h. (8)
The charged HiggsH± can be pair produced:
e+e− →H+H−. (9)
Figure 7 from [11] shows examples ofe+e− →Z+h, H and e+e− →A+h, H production cross-sections in the MSSM as functions of the respective Higgs masses for selected values of√
sand tanβ.
3.2.3 Decay of MSSM Higgs
Branching ratios of the lightest neutral Higgs differ from those in SM. Precision measurements can give indirect evidence for SUSY.R≡Γ(h→b¯b)/Γ(h→ττ¯) is sensitive to parameters of MSSM. This is shown in figure 8, taken from [27]. The inner band gives 5% experimental uncertainty. For large tanβ, it is sensitive to mA≤600 GeV for√
s= 350 GeV andL= 1000 fb−1.
Figure 7. Production cross-sections of the neutral Higgs bosons in the MSSM at √
s = 350 GeV in Higgsstrahlung and pair production processes for tanβ= 3 and 30 (from [11]).
Figure 8. Deviation of the ratioR≡Γ(h→bb)/Γ(h0 →τ τ) from the SM prediction. The expected experimental uncertainty,∼5%, is given by the inner bands (from [27]).
3.3 Search for supersymmetry at the linear collider
Supersymmetric extension of SM is the most theoretically motivated extension of SM. Supersymmetry is a symmetry of space–time that relates fermions and bosons.
It associates with every known particle a new particle differing in spin by 1/2. These new particles are collectively known as ‘sparticles’. Supersymmetry relates the cou- plings of the new particles to those of known particles. This leads to predictions for production and decay rates of sparticles in terms of their masses. Supersymmetry breaking leads to mass splitting while preserving coupling constant relations.
Observing new particles associated with supersymmetry is a major goal of both LHC and ILC. At hadron colliders, all kinematically allowed sparticles are produced together. It is difficult to disentangle the pattern of sparticle masses and couplings.
On the other hand, a lepton collider which can change the cm energy can explore spectrum of sparticles systematically. Scalar sparticles associated with leptons are particularly difficult to observe at hadron colliders.
3.3.1 Goals for the study of supersymmetry
The goals for the study of supersymmetry would be to discover all the predicted sparticles, to measure the sparticle quantum numbers, to measure their masses and to measure the sparticle couplings to establish supersymmetry. In addition, the above measurements should be able to unravel the supersymmetry breaking scheme.
3.3.2 Supersymmetric partners
In supersymmetric theories, there is a new scalar partner for each chiral fermion.
Each massive fermion has two scalar partners, labelled with suffixes L and R. In broken supersymmetry, these two partners can have different masses. Each gauge boson has a spin-1/2 partner (‘gaugino’). In SU(3)×SU(2)×U(1) these have masses denoted byM3, M2, M1 corresponding to the group factors. Higgs bosons have spin-1/2 partners called higgsinos. Charged gauginos and higgsinos mix to give charginos ˜χ±i , i= 1,2. Neutral gauginos and higgsinos mix to give neutralinos
˜
χ0i, i= 1, ...,4.
3.3.3 R parity and LSP
The most popular class of supersymmetric models hasRparity, a discrete symmetry imposed to prevent violation of lepton and baryon numbers. Because ofR parity, supersymmetric particles are always produced in pairs. The lightest supersymmet- ric particle (LSP) is stable. LSP is usually assumed to be the lightest neutralino.
LSP is also a viable candidate to explain dark matter in the Universe. ILC would be useful to test the candidacy of such a dark matter candidate by measuring its properties in detail [28].
3.3.4 Observation of sleptons
Scalar partners of leptons (sleptons ˜l±) can be produced throughs-channel γ and Z exchange
e+e− →γ, Z→˜l+˜l−. (10)
Selectron pair production has an additionalt-channel contribution from neutralino exchange. A slepton decays into a neutralino or chargino:
˜l± →χ˜0l±,χ˜±νl. (11)
Figure 9. Signal from e+e− → µ˜+Rµ˜−R → µ+µ−χ˜01χ˜01 and the dominant backgrounds formµ˜R = 132 GeV and mχ˜0
1 = 71.9 GeV,√
s= 320 GeV, and an integrated luminosity ofL= 160 fb−1(from [29]).
If the slepton decays to an LSP ( ˜χ01), the chain is
e+e− →˜l+˜l−→l+l−χ˜01χ˜01. (12) The momentum of leptons is precisely measured, whereas neutralinos give missing transverse momentum.
The energy distribution of decay leptons is directly related to slepton and neu- tralino masses:
m2˜l = sEminEmax
(Emin+Emax)2; 1−m2χ˜0
m2˜l = 2(Emin+Emax)
√s . (13)
The end-pointsEmin,Emaxafford a measurement of slepton masses. The end-points of the lepton energy spectrum can be clearly seen in figure 9 [29]. The situation is more complicated in the case of ˜τ sleptons due to the escaping neutrinos fromτ decay. If the neutralino mass is known from smuon decay, the shape can be used to determine the stau mass. The dominant background is from e+e− →W+W− → l+l0−νlν¯l0. However, it is strongly peaked in the forward direction. It can therefore be reduced by an angular cut. The background can also be reduced by the use of polarized beams (e−Re+L).
Slepton masses can also be measured precisely from threshold energy scans, in- dependent of the decay pattern. Because sleptons are scalars, threshold energy dependence scales like β3 as compared to β dependence for fermion pairs. The absolute cross-section for slepton pair production measures the slepton couplings to 1–2% accuracy.
3.3.5 Charginos and neutralinos
Charginos and neutralinos are pair produced:
e+e− →χ˜±i χ˜∓i , i= 1,2; (14)
Table 2. Sparticle masses and their expected precision for the SPS1a pa- rameters and for the case of supersymmetry breaking with universal masses (mSUGRA scenario) (adapted from [30]).
m LHC ILC LHC+ILC m LHC ILC LHC+ILC
h 111.6 0.25 0.05 0.05 H 399.6 1.5 1.5
A 399.1 1.5 1.5 H+ 407.1 1.5 1.5
χ01 97.03 4.8 0.05 0.05 χ02 182.9 4.7 1.2 0.08
χ03 349.2 4.0 4.0 χ04 370.3 5.1 4.0 2.3
χ±1 182.3 0.55 0.55 χ±2 370.6 3.0 3.0
˜
e1 144.9 4.8 0.05 0.05 ˜e2 204.2 5.0 0.2 0.2
˜
µ1 144.9 4.8 0.2 0.2 µ˜2 204.2 5.0 0.5 0.5
˜
τ1 135.5 6.5 0.3 0.3 ˜τ2 207.9 1.1 1.1
˜
νe 188.2 1.2 1.2
e+e− →χ˜0iχ˜0i, i= 1,4. (15) Chargino production occurs through s-channel Z exchange and t-channel sneu- trino exchange. The lightest chargino decays according to ˜χ±1 →l±νlχ˜01 either via intermediateW± or via slepton. The dominant background isW W andZZ pro- duction, which can be minimized using beam polarization. The chargino mass can be measured through the kinematic end-points of the decay products and through a threshold scan.
The second lightest neutralino decays according to ˜χ02→l+l−χ˜01 either viaZ or via a slepton. The energy spectrum of the di-lepton system can be used to determine the masses of the primary and secondary neutralino, as in the case of slepton.
˜
χ02’s are also produced in decay chains. One can get a precise mass difference
∆m( ˜χ02−χ˜01) from the upper edge of the di-lepton mass spectrum. Charginos with the decay ˜χ±1 →q¯q0χ˜01give ∆m( ˜χ±1 −χ01).
To give an idea of the precision of mass determination at ILC, sparticle masses and their expected precision for the point in parameter space known as SPS1a and for the case of supersymmetry breaking with universal masses (mSUGRA scenario) are shown in table 2.
3.3.6 SUSY with CP violation
There can be complex phases in various mass matrices in MSSM. This can lead to observable effects like electric dipole moments of fermions, which, due to the existing experimental limits, constrain the parameters of the theory. In addition, the presence of phases can affect the determination of the range of MSSM pa- rameters from experimental information on even CP-conserving processes. In [31]
production and decays of the third generation sfermions in the MSSM with complex parameters have been analysed. In a large region of the MSSM parameter space the branching ratios of these sfermions show a strong phase dependence. This could
4. Theories with extra dimensions at the linear collider
In recent times, theories with extra dimensions have seen revived interest because of the possibility that an effective Planck scale can exist at TeV energy in such theories. There are three classes of extra-dimension models, differing from each other in the geometry of various fields. They have different experimental signatures.
The common feature of all such models is the presence of closely spaced excitations extending into the TeV mass range and particles with spin-2. These are well-suited for study ine+e− collisions at the highest possible energies. Moreover, it has been proposed that the e−e−, e−γ, and γγ options and the possibility of transverse polarization can be used to differentiate extra-dimension models.
4.1 The ADD model
In the original extra dimensions model in the recent context, the so-called ADD model due to Arkani-Hamed, Dimopoulos, and Dvali [37], SM fields are confined to a 1+3-dimensional brane. Gravity propagates in the ‘bulk’ of the other dimensions.
Gravity is strong in the bulk, but only a fraction is felt on the brane. The relation between the Planck scaleMPlanckand the compactification radiusR is given, ford extra dimensions, by
MPlanck2 ∼Mbraned+2 Rd, (16)
whereMbraneis the effective Planck mass scale on the 3-brane where SM lives. The effective Planck mass can be tuned to the TeV scale. Ford= 2,R is on the order of a millimeter.
There is a tower of excited Kaluza–Klein (KK) graviton states which couple weakly to SM particles. Ine+e−collisions the experimental signature for the model is missing energy in SM processes by radiation of a KK graviton from SM particles [38], or a change in the rate and angular distribution of pair production by virtue of the graviton propagator [39]. One signature of the first kind is missing energy in e+e− → γ+ missing energy [40]. Another is a radiated graviton in Bhabha scattering [41]. Clean measurement of the angular distribution of final states in γ+ missing energy would distinguish the ADD model from a scenario where the missing energy is from extra neutrinos or superpartners.
Figure 10. The cross-section for the production of a graviton and neutral gauge KK excitations ine+e−as a function of the c.m. energy√
sfor a model having first KK excitation at 500 GeV. The different curves correspond to various values ofκ/M¯Planck (from [43]).
4.2 Randall–Sundrum model
The Randall–Sundrum (RS) model allows for a brane having a TeV scale without large compactification radius of extra dimensions [42]. There is one extra dimension and two branes, one with an effective Planck mass at TeV scale and the other at the Planck scale. A scalar field in the bulk keeps the branes the proper distance apart. This results in a warp factor e−πκR for the space–time metric, where κ is the curvature of fifth dimension and R is the compactification scale. A TeV scale on the low-energy brane is achieved ifκR∼12. Graviton masses are of electroweak scale, and there is a series of KK gravitons. The masses of the KK excitations of the gravitons areMn=ζnm0, wherem0=κe−πκR andζn are zeroes of the Bessel function [43]. Other schemes lead to different mass spacings. It is more useful to consider model parameters as m0 and c0 = κ/M¯Planck, the effective coupling.
The gravitons have weak strength and decay into pairs of SM particles with a width dependent onc0. Figure 10, taken from [43], shows the cross-section for the e+e− production of graviton and neutral gauge KK excitations for a model having the first KK excitation at 500 GeV. The series of curves represents various values ofκ/M¯Planck. The gravitons have weak strength and decay into pairs of standard model particles with a width dependent onc0. Thus, because of the good resolution of ane+e− collider, the excitations can be easily observed.
The difference between ADD and RS in the production of single photons vs.
dimuons at √
s=2 TeV is shown in figure 11, taken from [44]. It is thus possible to distinguish between the two scenarios.
4.3Universal extra dimensions
In the model with universal extra dimensions (UED), all SM fields live in the extra- dimensional bulk. Thus, all SM particles have KK excitations [45]. In UED models,
Figure 11. Cross-sections for the production of single photons and of dimuons at√
s =2 TeV are plotted against each other. ADD lines are for extra dimensions of 3 and 6. The RS curves are form0 = 200 and 400 GeV (from [44]).
there is a conservation of KK mode number. Thus, at lowest order, excited particles are produced in pairs. The lightest KK particle is the photon with n = 0. This model is similar to SUSY to the extent that every SM particle has a tower of KK- partners, even though these partners have the same spin. Determining whether one is seeing UED or SUSY will require excellent determination of angular distributions.
5. Models with extra Z at the linear collider
There are several models with extra neutral gauge bosonZ0, as for example, grand unification (E6ξ models), left–right symmetry [30,46–48] KK excitations ofγ and Z [49] and little Higgs model(s) [50].
ILC can make precision measurements of various observables in e+e− → ff¯: σ0 ≡ σ(e+e− → µ+µ−), Rhad ≡ σhad/σ0, AlFB, AlLR, AhadLR, Aτpol, and AfFB(pol).
Here the notation is standard; the subscript ‘had’ refers to hadronic cross-sections,
‘FB’ refers to ‘forward–backward’, ‘LR’ to ‘left–right’ (asymmetry) in the context of longitudinal polarization of beams, and ‘pol’ to the polarized beams.
Beam polarization with Pe− and Pe+ of opposite signs helps to enhance cross- section, as seen from eq. (1). With √
s = 500 GeV, L = 1 ab−1, Pe− = 0.8, Pe+ = 0.6,mZ0 up to 2–3 TeV can be probed at 95% CL. It is found that there is an ambiguity if only leptonic final states are used [51]. It is resolved if hadronic states are included in addition to leptonic states [52]. In any case beam polarization plays an important role [52].
6. Conclusions
To conclude, a description has been given of various physics capabilities of ane+e− linear collider and its options. It is clear that a lot of precision information within
SM and beyond would become available with such a collider. With the determined effort of the international high energy physics community, ILC seems certain to become a reality.
References
[1] American Linear Collider Working Group: J Baggeret al, arXiv:hep-ex/0007022 ACFA Linear Collider Working Group: K Abeet al, arXiv:hep-ph/0109166
ECFA/DESY LC Physics Working Group: J A Aguilar-Saavedra et al, arXiv:hep- ph/0106315
A Bartl and S Hesselbach, Pramana – J. Phys. 63, 1101 (2004); arXiv:hep- ph/0407178
S Dawson and M Oreglia, Ann. Rev. Nucl. Part. Sci. 54, 269 (2004); arXiv:hep- ph/0403015
[2] G A Moortgat-Picket al, arXiv:hep-ph/0507011
[3] I F Ginzburg, G L Kotkin, V G Serbo and V I Telnov,Nucl. Instrum. Methods205, 47 (1983)
[4] I F Ginzburg, G L Kotkin, S L Panfil, V G Serbo and V I Telnov,Nucl. Instrum.
MethodsA219, 5 (1984)
V I Telnov,Nucl. Instrum. MethodsA355, 3 (1995) [5] W Menges, LC-PHSM-2001-022
[6] D Choudhury and S D Rindani,Phys. Lett.B335, 198 (1994); arXiv:hep-ph/9405242 B Ananthanarayan, S D Rindani, R K Singh and A Bartl, Phys. Lett. B593, 95 (2004); Erratum,ibidB608, 274 (2005); arXiv:hep-ph/0404106
[7] A H Hoang, A V Manohar, I W Stewart and T Teubner, Phys. Rev. D65, 014014 (2002); arXiv:hep-ph/0107144
[8] A H Hoang,Phys. Rev.D69, 034009 (2004); arXiv:hep-ph/0307376
[9] A H Hoang and T Teubner,Phys. Rev.D60, 114027 (1999); arXiv:hep-ph/9904468 A H Hoang, Z Ligeti and A V Manohar,Phys. Rev. Lett.82, 277 (1999); arXiv:hep- ph/9809423
[10] M Martinez and R Miquel,Eur. Phys. J.C27, 49 (2003); arXiv:hep-ph/0207315 [11] A Djouadi,Pramana – J. Phys.60, 215 (2003); arXiv:hep-ph/0205248
[12] T Kuhl, http://www-flc.desy.de/ecfa-higgs/montpellier/kuhl-montpellier.pdf [13] M Battaglia and A De Roeck, in Proc. of the APS/DPF/DPB Summer Study on
the Future of Particle Physics (Snowmass 2001) edited by N Graf, eConfC010630, E3066 (2001); arXiv:hep-ph/0111307
[14] A Juste and G Merino, arXiv:hep-ph/9910301 A Gay, arXiv:hep-ph/0604034
H Baer, S Dawson and L Reina, Phys. Rev. D61, 013002 (2000); arXiv:hep- ph/9906419
[15] U Baur, T Plehn and D L Rainwater, Phys. Rev. D68, 033001 (2003); arXiv:hep- ph/0304015
C Castanier, P Gay, P Lutz and J Orloff, arXiv:hep-ex/0101028
M Battaglia, E Boos and W M Yao, inProc. of the APS/DPF/DPB Summer Study on the Future of Particle Physics (Snowmass 2001) edited by N Graf, eConfC010630, E3016 (2001); arXiv:hep-ph/0111276
[16] A Djouadi, W Kilian, M Muhlleitner and P M Zerwas,Euro. Phys. J.C10, 27 (1999);
arXiv:hep-ph/9903229
ph/9606356; Phys. Rev. D54, 4326 (1996); Erratum, ibid. D61, 119901 (2000);
arXiv:hep-ph/9509299;Phys. Lett.B349, 379 (1995); arXiv:hep-ph/9410357 F Cuypers and S D Rindani,Phys. Lett.B343, 333 (1995); arXiv:hep-ph/9409243 [22] D Atwood, S Bar-Shalom, G Eilam and A Soni,Phys. Rep. 347, 1 (2001); arXiv:hep-
ph/0006032
[23] P Poulose and S D Rindani, Phys. Rev. D57, 5444 (1998); Erratum, ibid. D61, 119902 (2000); arXiv:hep-ph/9709225
[24] M S Baek, S Y Choi and C S Kim, Phys. Rev. D56, 6835 (1997); arXiv:hep- ph/9704312
S Y Choi and K Hagiwara,Phys. Lett.B359, 369 (1995); arXiv:hep-ph/9506430 [25] B Grzadkowski, Z Hioki, K Ohkuma and J Wudka, Acta Phys. Polon. B36, 3531
(2005); arXiv:hep-ph/0511038
B Grzadkowski, Z Hioki, K Ohkuma and J Wudka, Nucl. Phys. B689, 108 (2004);
arXiv:hep-ph/0310159
[26] B C Allanach, A Djouadi, J L Kneur, W Porod and P Slavich,J. High Energy Phys.
0409, 044 (2004); arXiv:hep-ph/0406166
[27] J Guasch, W Hollik and S Penaranda, arXiv:hep-ph/0307012;Phys. Lett.B515, 367 (2001); arXiv:hep-ph/0106027
[28] S Kraml, these proceedings
[29] H U Martyn and G A Blair, arXiv:hep-ph/9910416.
[30] LHC/LC Study Group: G Weigleinet al, arXiv:hep-ph/0410364
[31] A Bartl, K Hidaka, T Kernreiter and W Porod, Phys. Lett. B538, 137 (2002);
arXiv:hep-ph/0204071;Phys. Rev.D66, 115009 (2002); arXiv:hep-ph/0207186 A Bartl, S Hesselbach, K Hidaka, T Kernreiter and W Porod, arXiv:hep-ph/0306281;
Phys. Lett.B573, 153 (2003); arXiv:hep-ph/0307317; arXiv:hep-ph/0311338 [32] S Y Choi, H S Song and W Y Song, Phys. Rev. D61, 075004 (2000); arXiv:hep-
ph/9907474
[33] Y Kizukuri and N Oshimo,Phys. Lett.B249, 449 (1990)
A Bartl, H Fraas, S Hesselbach, K Hohenwarter-Sodek and G Moortgat-Pick, arXiv:hep-ph/0406190
A Bartl, H Fraas, O Kittel and W Majerotto, Phys. Rev. D69, 035007 (2004);
arXiv:hep-ph/0308141
A Bartl, H Fraas, O Kittel and W Majerotto, arXiv:hep-ph/0402016 [34] A Pilaftsis,Phys. Lett.B435, 88 (1998); arXiv:hep-ph/9805373
A Pilaftsis and C E M Wagner,Nucl. Phys.B553, 3 (1999); arXiv:hep-ph/9902371 [35] R M Godbole, S D Rindani and R K Singh,Phys. Rev.D67, 095009 (2003); Erratum,
ibid.D71, 039902 (2005)
[36] E Asakawa, S Y Choi, K Hagiwara and J S Lee, Phys. Rev. D62, 115005 (2000);
arXiv:hep-ph/0005313
J R Ellis, J S Lee and A Pilaftsis, Nucl. Phys. B718, 247 (2005); arXiv:hep- ph/0411379
[37] N Arkani-Hamed, S Dimopoulos and G R Dvali, Phys. Lett. B429, 263 (1998);
arXiv:hep-ph/9803315;Phys. Rev.D59, 086004 (1999); arXiv:hep-ph/9807344 I Antoniadis, N Arkani-Hamed, S Dimopoulos and G R Dvali,Phys. Lett.B436, 257 (1998); arXiv:hep-ph/9804398
[38] O J P Eboli, M B Magro, P Mathews and P G Mercadante,Phys. Rev.D64, 035005 (2001); arXiv:hep-ph/0103053
[39] G F Giudice, R Rattazzi and J D Wells, Nucl. Phys. B544, 3 (1999); arXiv:hep- ph/9811291
T Han, J D Lykken and R J Zhang, Phys. Rev. D59, 105006 (1999); arXiv:hep- ph/9811350
K Agashe and N G Deshpande,Phys. Lett.B456, 60 (1999); arXiv:hep-ph/9902263 K M Cheung and G Landsberg, Phys. Rev. D65, 076003 (2002); arXiv:hep- ph/0110346
[40] E A Mirabelli, M Perelstein and M E Peskin, Phys. Rev. Lett. 82, 2236 (1999);
arXiv:hep-ph/9811337
S Gopalakrishna, M Perelstein and J D Wells, inProc. of the APS/DPF/DPB Sum- mer Study on the Future of Particle Physics (Snowmass 2001) edited by N Graf, eConfC010630, P311 (2001); arXiv:hep-ph/0110339
[41] S Dutta, P Konar, B Mukhopadhyaya and S Raychaudhuri,Phys. Rev.D68, 095005 (2003); arXiv:hep-ph/0307117
[42] L Randall and R Sundrum,Phys. Rev. Lett.83, 4690 (1999); arXiv:hep-th/9906064 [43] H Davoudiasl, J L Hewett and T G Rizzo,Phys. Rev.D63, 075004 (2001); arXiv:hep-
ph/0006041
[44] S K Rai and S Raychaudhuri, J. High Energy Phys. 0310, 020 (2003); arXiv:hep- ph/0307096
[45] T Appelquist and B A Dobrescu,Phys. Lett.B516, 85 (2001); arXiv:hep-ph/0106140 [46] S Capstick and S Godfrey,Phys. Rev.D37, 2466 (1988)
S Godfrey,Phys. Rev.D51, 1402 (1995); arXiv:hep-ph/9411237 [47] A Leike,Phys. Rep.317, 143 (1999); arXiv:hep-ph/9805494
M Cvetic and S Godfrey, arXiv:hep-ph/9504216
[48] ECFA/DESY LC Physics Working Group: J A Aguilar-Saavedra et al, arXiv:hep- ph/0106315
[49] T G Rizzo, eConfC040802, L013 (2004); arXiv:hep-ph/0409309 K Cheung, arXiv:hep-ph/0409028
[50] N Arkani-Hamed, A G Cohen, E Katz and A E Nelson,J. High Energy Phys.0207, 034 (2002); arXiv:hep-ph/0206021
M Schmaltz,J. High Energy Phys.0408, 056 (2004); arXiv:hep-ph/0407143 M Schmaltz and D Tucker-Smith, Ann. Rev. Nucl. Part. Sci. 55, 229 (2005);
arXiv:hep-ph/0502182
T Han, H E Logan, B McElrath and L T Wang, Phys. Rev. D67, 095004 (2003);
arXiv:hep-ph/0301040
T Han, H E Logan and L T Wang,J. High Energy Phys.0601, 099 (2006); arXiv:hep- ph/0506313
[51] S. Riemann in ref. [48]
[52] S Godfrey, P Kalyniak and A Tomkins, arXiv:hep-ph/0511335
